The constant current field of wide-area layered earth has adverse effects on many industries. But it presents a high degree of numerical singularity, resulting in difficulty in solving. In this paper, the derivation of Green’s function and the fast Hankel transformation are presented based on the basic principle of linear filtering method for Green’s function of wide-area layered earth. A method of Multi-Precision Fast Hankel Transformation (MP-FHT) is proposed, which solves the problem of numerical singularity of integral kernel function in Green’s function by multi-precision algorithm, thus ensuring the accuracy of Hankel integral. The accuracy and reliability of the MP-FHT are proved by comparison of MP-FHT, commercial software CDEGS and improved version of high-order complex image method (HCIM). Compared with the existing algorithms, this method has high precision and low difficulty in algorithm implementation, which is a new method with high practical value.
WenXLiuCLiWPanZCaiHHuS. Computation for wide-area direct current distribution of power grids considering deep earth resistivity. High Voltage Engineering.2017; 43(7): 2331-9. doi: 10.13336/j.1003-6520.hve.20170628031. (in Chinese)
2.
YangNChenYPanZWenX. Influence prediction and suppression research of dc bias in eastern Junggar-Southern Anhui ± 1100 kV UHVDC receiving-end grid. Power System Technology.2018; 42(2): 381-7. doi: 10.13335/j.1000-3673.pst.2017.2192. (in Chinese)
3.
CaiLWangJFanYZhouMGongMLiuS. Influence of the track-to-earth resistance of subway on stray current distribution. High Voltage Engineering.2015; 41(11): 3604-10. doi: 10.13336/j.1003-6520.hve.2015.11.012. (in Chinese)
4.
LiuLYangPGuoSLiuCMaC. Impact of geoelectric field direction and ac system structure on geomagnetically induced currents in ± 800 kV Mengxi convertor station. Power System Technology.2015; 40(5): 1295-300. doi: 10.13335/j.1000-3673.pst.2016.05.001. (in Chinese)
5.
QuanJTongXWenXXuBRuanLPanZ. Mitigation of transformer dc bias in complicated operation conditions. High Voltage Engineering.2015; 41(7): 2464-72. doi: 10.13336/j.1003-6520.hve.2015.03.012. (in Chinese)
6.
MengXCaoFLiaoYLiRZhangB. Analysis of insulation methods to reduce influences of dc grounding electrode on pipeline. High Voltage Engineering.2017; 43(12): 3900-3906. doi: 10.13336/j.1003-6520.hve.20171127011. (in Chinese)
7.
ZhangW. Corrosion damage mechanism of reinforced concrete structures caused by the stray current of rail transit system. Harbin: Harbin Institute of Technology;2017. (in Chinese)
8.
TangBZhangXGeGZhangJLiuXQuZ. Interference on geoelectric field observation from UHVDC power lines and its ground electrode. High Voltage Engineering.2013; 39(12): 2951-2959. doi: 10.3969/j.issn.1003-6520.2013.12.016(in. Chinese)
9.
PanZZhangLLiuHLuHWenX. Simulation and analysis of earth surface potential distribution in horizontal multi-layer soil. High Voltage Engineering.2012; 38(1): 116-123. doi: 10.3969/j.issn.1003-6520.2012.01.017. (in Chinese)
10.
XiD. Bessel function. Beijing: Higher Education Press;1998; (in Chinese).
11.
LukeL. Integrals of Bessel functions. New York: McGraw-Hill Book Company. Inc, 1962.
12.
LiWPanZLuHChenXZhangLWenX. Influence of deep earth resistivity on HVDC ground-return currents distribution. IEEE Transactions on Power Delivery.2017; 32(4): 1844-51. doi: 10.1109/TPWRD.2016.2610443.
13.
ZouJDuXZhouC. Fast calculation of the Green function of a point current source in a horizontal layered soil with a new complex path and its application in grounding system. IEEE Transactions on Magnetics.2015; 51(3): 1-4. doi: 10.1109/TMAG.2014.2350486.
14.
ZhangBYuanJZouJLeeJJuMN. Semianalytical approach to the inverse Fourier transform and its application in evaluating lightning horizontal electric field. IEEE Transactions on Electromagnetic Compatibility.2016; 58(2): 477-86. doi: 10.1109/TEMC.2015.2513083.
15.
RizkMEMMahmoodFLehtonenMBadranEAAbdel-RahmanMH. Computation of peak lightning-induced voltages due to the typical first and subsequent strokes considering high ground resistivity. IEEE Transactions on Power Delivery.2017; 32(4): 1861-71. doi: 10.1109/TPWRD.2016.2555856.
16.
HeJ. Power system grounding technology. Beijing: Science Press; 2007; (in Chinese)
17.
ChenDHuangZLiuJ, et al. Calculation of current field due to a point source in multi-layer soil. High Voltage Engineering.2008; 34(7): 1379-82. (in Chinese)
18.
XieG. Power System Grounding Technology. Beijing: Hydro Power Press; 1991; (in Chinese)
19.
ChenZ. Electrical exploration. Beijing: Metallurgical Industry Press; 2015; (in Chinese)
20.
ChowYYangJSrivastavaK. Complex image of a grounding electrode in layered soils. Journal of Applied Physics.1992; 1(1): 1120-25.
21.
HeWZhangRYangFZhuLLiuZWangX. Parameter estimation of horizontal multi-layer earth in substation. Proceedings of the CSEE.2014; 39(33): 5964-73. doi: 10.13334/j.0258-8013.pcsee.2014.33.021 (in Chinese)
22.
ZhuXZhaoSJiaH. Improved prony method based on higher-order cumulant for low frequency oscillation detection. Proceedings of the CSU-EPSA.2017; 29(9): 1-8.
23.
AbramowitzMStegunI. Handbook of mathematical functions. New York: Dover. 1970.
24.
HuaYSarkarT. Generalized pencil-of-function method for extracting poles of an EM system from its transient response. IEEE Transactions on Antennas and Propagation.1989; 37(2): 229-34. doi: 10.1109/8.18710.
25.
TapanTOdilonP. Using the matrix pencil method to estimate the parameters of a sum of complex exponentials. IEEE Antennas and Propagation Magazine.1995; 37(1): 48-55. doi: 10.1109/74.370583.
26.
SheshyekaniKTabeiB. Multiport frequency-dependent network equivalent using a modified matrix pencil method. IEEE Transactions on Power Delivery.2014; 29(5): 2340-8. doi: 10.1109/TPWRD.2014.2323335.
27.
LiuSLiCShiYQianCLiuL. Calculation of dc current caused by dc ground electrode in traction transformer of electrified railway. High Voltage Engineering.2017; 43(7): 2161-6. doi: 10.13336/j.1003-6520.hve.20170628009. (in Chinese)
28.
KoefoedODirksF. Determination of resistivity sounding filters by the Wiener-Hopf least-squares method. Geophysical Prospecting.1979; 27(1): 245-50.
29.
AndersonW. Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering. Geophysicists.1979; 44(4): 1287-305.
30.
AndersonW. Fast Hankel transforms using related and lagged convolutions. ACM Transactions on Mathematical Software.1982; 8(4): 344-68.
31.
AndersonW. A hybrid fast Hankel transform algorithm for electromagnetic modelling. Geophysicists.1989; 542): 263-6.
32.
GuptasarmaDSinghD. New digital linear filters for Hankel J0 and J1 transforms. 1997; 45(5): 745-62.
33.
KongF. Hankel transform filters for dipole antenna radiation in a conductive medium. Geophysical Prospecting.2007; 55(1): 83-9. doi: 10.1111/j.1365-2478.2006.00585.x.
34.
WangXRuanLWenXQuanJPanZLuH. Characteristics analysis of dc-bias currents considering deep-earth resistivity. High Voltage Engineering.2015; 41(5): 1536-1543. doi: 10.13336/j.1003-6520.hve.2015.05.016. (in Chinese)
35.
JiangH. Study on reliable computing and rounding error analysis in floating-point arithmetic. Changsha: National University of Defense Technology; 2013; (in Chinese)
36.
MullerJBrisebarreNDinechinFJeannerodCPLefevreVMelquiondG, et al. Handbook of floating-point arithmetic. Birkhäuser.2018; pp. 44-91.
37.
DanielMBohušU. Numerical approach for computation of electromagnetic shielding. Journal of Electrical Engineering.2013; 64(4): 256-260.
38.
The GNU multiple precision arithmetic library. Online available from: https://gmplib.org.
